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ó rKXc @ s d d l m Z d d l m Z d d l m Z d e f d YZ d e f d YZ e d d d Z d Z e d k r e n d S( i’’’’( t divisioni ( t print_( t numbertheoryt CurveFpc B s; e Z d Z d Z d Z d Z d Z d Z RS( s9 Elliptic Curve over the field of integers modulo a prime.c C s | | _ | | _ | | _ d S( s; The curve of points satisfying y^2 = x^3 + a*x + b (mod p).N( t _CurveFp__pt _CurveFp__at _CurveFp__b( t selft pt at b( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyt __init__* s c C s | j S( N( R ( R ( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyR 0 s c C s | j S( N( R ( R ( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyR 3 s c C s | j S( N( R ( R ( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyR 6 s c C s3 | | | | | | j | | j | j d k S( s! Is the point (x,y) on this curve?i ( R R R ( R t xt y( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyt contains_point9 s ( t __name__t __module__t __doc__R R R R R ( ( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyR ( s t Pointc B st e Z d Z d d Z d Z d Z d Z d Z d Z d Z d Z d Z d Z d Z RS( ss A point on an elliptic curve. Altering x and y is forbidding, but they can be read by the x() and y() methods.c C sn | | _ | | _ | | _ | | _ | j rK | j j | | sK t n | rj | | t k sj t n d S( s@ curve, x, y, order; order (optional) is the order of this point.N( t _Point__curvet _Point__xt _Point__yt _Point__orderR t AssertionErrort INFINITY( R t curveR R t order( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyR B s c C sB | j | j k r: | j | j k r: | j | j k r: t St Sd S( s9 Return True if the points are identical, False otherwise.N( R R R t Truet False( R t other( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyt __eq__L s c C s | t k r | S| t k r | S| j | j k s8 t | j | j k r~ | j | j | j j d k rq t S| j Sn | j j } | j | j t j | j | j | | } | | | j | j | } | | j | | j | } t | j | | S( s Add one point to another point.i ( R R R R R R t doubleR t inverse_modR ( R R R t lt x3t y3( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyt __add__U s # !c C s# d } | } | j r( | | j } n | d k r8 t S| t k rH t S| d k sZ t d | } t | j | j | j | j } | | d } | } x | d k r| j } | | @d k rä | | @d k rä | | } n | | @d k r| | @d k r| | } n | d } q W| S( s Multiply a point by an integer.c S s= | d k s t d } x | | k r4 d | } q W| d S( Ni i i ( R ( R t result( ( sY C:\Program Files\MySQL\MySQL Workbench 6.3 CE/python/site-packages\ecdsa\ellipticcurve.pyt leftmost_bitp s i i i i ( R R R R R R R R ( R R R&